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Bibliographic Details
Main Authors: Rao, Hui, Xu, Yan-Li, Zhang, Yuan
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2501.02426
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Table of Contents:
  • Doubling measure was introduced by Beurling and Ahlfors in 1956 and now it becomes a basic concept in analysis on metric space. In this paper, for a measure which is not doubling, we introduce a notion of point-wise doubling index, and calculate the point-wise doubling indices of uniform Bernoulli measures on Bedford-McMullen carpets. As an application, we show that, except a small class of Bedford-McMullen carpets, if two Bedford-McMullen carpets are bi-Lipschitz equivalent, then they have the same fiber sequence up to a permutation.